I don't have the answer to all of these, but I can answer a couple.
The info about what you've read is stored on the e-reader. It must be, since I run my KT in "airplane mode" (wifi off) all the time, and I've never connected it to a wifi connection. PeterT says it's SQLite.
"Book Cover" means whether it displays the cover of the book you're reading/last read when it's in sleep mode or off. I have it on, so even in sleep mode, I see the cover of the book I was last reading. If you turn that feature off, you should get a cartoony Kobo with closed eyes, smiling, and saying "sleep mode" or "powered off."
I can't help you with the turning on issue - I haven't had that problem.
In terms of cases, there are some other models whose cases will fit the Kobo. I have an M-Edge Nook Touch case that fits the KT perfectly. The covers are re-enforced, so it's pretty protective. Other people have used Sony cases (forget which model). There's also some fairly cheap Kobo Touch-specific cases on SkinDigitalStore.com. I think they sell an easel-style case for about $15 in non-girlie colors.
